The Stabilities of phase What is a phase? A phase is a form of matter that is uniform throughout in chemical composition and physical state Example Fig 1. White phosphorus Fig 2.Black phosphorus Fig 3. Liquid phase A phase transition is the spontaneous conversion of one phase into another phase,occurs at a characteristic temperature for a given presure Example At 1 atm Below 00C Ice Above 00C Liquid water Fig 4. The example of phase transition The transition temperature,Ttrs, is the temperature at which the two phase are in equilibrium and the Gibbs energy is minimized at the prevailing presure Example Fig 5. The transition temperature of water A metastable phase is a thermodynamically unstable phase that persists because the transition is kinetically hindered Example Diamond Fig 6. Metastable phase of carbon Graphite Fig 7. A metastable systems diagram Phase boundaries A phase diagram is a diagram show the regions of pressure and temperature at which its various phase are thermodynamically stable Fig 8. A typical phase diagrams Fig 10. The boiling process Heat The temperature at which the vapour pressure of a liquid is equal to the external pressure is called the boiling temperature Fig 9. The experiment about vapour pressure Heat Heat Fig 11. The experiment about critical temperature The temperature at which the surface disappear is the critical temperature Melting Freezing The melting temperature (or freezing temperature) is the temperature at which, under the specified pressure, the liquid and solid phases of a substance coexist in equilibrium Phase Diagrams ISSUES TO ADDRESS... • When we combine two elements... what equilibrium state do we get? • In particular, if we specify... ‐‐a composition (e.g., wt% Cu ‐ wt% Ni), and ‐‐a temperature (T) then... How many phases do we get? What is the composition of each phase? How much of each phase do we get? Phase B Phase A Nickel atom Copper atom Phase Equilibria: Solubility Limit Introduction – Solutions – solid solutions, single phase – Mixtures – more than one phase Sucrose/Water Phase Diagram • Solubility Limit: Answer: 65 wt% sugar. If Co < 65 wt% sugar: syrup If Co > 65 wt% sugar: syrup + sugar. 60 L 40 (liquid solution i.e., syrup) 20 0 L (liquid) + S (solid sugar) 20 40 60 65 80 Co =Composition (wt% sugar) 100 Pure Sugar solubility limit at 20°C? Solubility Limit 80 Pure Water Question: What is the 10 0 Temperature (°C) Max concentration for which only a single phase solution occurs. Components and Phases • Components: The elements or compounds which are present in the mixture (e.g., Al and Cu) • Phases: The physically and chemically distinct material regions that result (e.g., α and β). Aluminum‐ Copper Alloy β (lighter phase) α (darker phase) Effect of T & Composition (Co) • Changing T can change # of phases: • Changing Co can change # of phases: path A to B. path B to D. B (100°C,70) 1 phase D (100°C,90) 2 phases water‐ sugar system Temperature (°C) 100 80 L 60 (liquid) + L (liquid solution 40 i.e., syrup) 20 0 0 S (solid sugar) A (20°C,70) 2 phases 20 40 60 70 80 Co =Composition (wt% sugar) 100 Phase Equilibria Simple solution system (e.g., Ni‐Cu solution) Crystal Structure electro negativity r (nm) Ni FCC 1.9 0.1246 Cu FCC 1.8 0.1278 •Both have the same crystal structure (FCC) and have similar electronegativities and atomic radii (W. Hume – Rothery rules) suggesting high mutual solubility. • Ni and Cu are totally miscible in all proportions. Phase Diagrams • Indicate phases as function of T, Co, and P. • For this course: ‐binary systems: just 2 components. ‐independent variables: T and Co (P = 1 atm is almost always used). • Phase Diagram for Cu‐Ni system T(°C) 1600 • 2 phases: 1500 L (liquid) α (FCC solid solution) L (liquid) • 3 phase fields: L L+ α α 1400 1300 α 1200 (FCC solid 1100 1000 solution) 0 20 40 60 80 100 wt% Ni Phase Diagrams: # and types of phases • Rule 1: If we know T and Co, then we know: ‐‐the # and types of phases present. T(°C) 1600 • Examples: B (1250°C,35) 1500 A(1100°C, 60): 1 phase: α B (1250°C, 35): 2 phases: L + L (liquid) 1400 α 1300 1200 α (FCC solid solution) A(1100°C,60) 1100 1000 Cu‐Ni phase diagram 0 20 40 60 80 100 wt% Ni Phase Diagrams: composition of phases • Rule 2: If we know T and Co, then we know: ‐‐the composition of each phase. • Examples: C o = 35 wt% Ni At T A = 1320°C: Only Liquid (L) C L = C o ( = 35 wt% Ni) At T D = 1190°C: Only Solid ( α) C α = C o ( = 35 wt% Ni ) Cu‐Ni system T(°C) A TA L (liquid) 1300 B TB 1200 D TD At T B = 1250°C: Both α and L C L = C liquidus ( = 32 wt% Ni here) C α = C solidus ( = 43 wt% Ni here) tie line 20 3032 35 C LC o α (solid) 40 4 3 50 C α wt% Ni Phase Diagrams: weight fractions of phases • Rule 3: If we know T and Co, then we know: ‐‐the amount of each phase (given in wt%). • Examples: C o = 35 wt% Ni At T A : Only Liquid (L) W L = 100 wt%, W α = 0 At T D : Only Solid ( α) W L = 0, W α = 100 wt% At T B : Both α and L WL = Wα = 43 − 35 = = 73 wt % R + S 43 − 32 S R R + S T(°C) A TA 1300 TB tie line L (liquid) B R 1200 S D TD 20 = 27 wt% Cu‐Ni system 3 032 35 C LC o α (solid) 4043 50 C α wt% Ni The Lever Rule • Tie line – connects the phases in equilibrium with each other ‐ essentially an isotherm T(°C) How much of each phase? Think of it as a lever tie line 1300 L (liquid) B TB α (solid) 1200 R 20 30C S 40 C α L Co R 50 wt% Ni WL = Mα ML C − C0 ML S = = α M L + M α R + S C α − CL S M α ⋅S = M L ⋅R Wα = C − CL R = 0 R + S C α − CL Fe‐Fe3C System 21
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